Class 8 Computational Thinking & AI
Official CBSE Student Handbook curriculum with 110 interactive practice questions, exponential thinking puzzles, quadrilateral spatial proofs, and responsible AI frameworks.
A Square and a Cube
A Square and a Cube develops algorithmic abstraction and algebraic number theory through powers, square/cube number patterns, and constraint satisfaction grids.
Practice Questions (20)
Click an option to test your answerFind the smallest natural number by which 392 must be multiplied to make it a perfect cube.
Hint: Factor 392 = 2^3 x 7^2. Which prime power needs topping up to the next multiple of 3?
A solid wooden cube has side 5 cm. It is painted red on all faces and then cut into 1 cm unit cubes. How many unit cubes have NO painted face at all?
Hint: The inner core of an n-cube (after painting and cutting) has side (n - 2).
Which of the following is NOT a perfect square?
Hint: Compute the square root of each option and check for a whole-number result.
What is the smallest natural number that must be added to 2000 to make it a perfect square?
Hint: Find the next perfect square above 2000: 45^2 = 2025.
The area of a square field is 7056 m^2. Find its perimeter.
Hint: Find the side length using the square root, then multiply by 4.
Which of the following is NOT a valid representation of 729?
Hint: Verify each: 3^6 = 729, 9^3 = 729, 27^2 = 729, 6^4 = ?
The product of three consecutive natural numbers is 504. What is the cube of the smallest of these three numbers?
Hint: Guess consecutive triples near the cube root of 504 (approximately 7.96).
How many perfect squares lie strictly between 50 and 250?
Hint: Find the smallest integer whose square exceeds 50, and the largest whose square is below 250.
What is the value of sqrt(225) + cube_root(512)?
Hint: Compute the square root of 225 and the cube root of 512 separately.
A Pythagorean triplet is generated by the formula (2m, m^2 - 1, m^2 + 1). If the smallest member is 20, what is the LARGEST member of the triplet?
Hint: If 20 = 2m, then m = 10. Compute m^2 - 1 and m^2 + 1.
What is the smallest natural number 'k' such that 3,600 × k is a perfect cube?
Hint: Find the prime factors of 3600 and check which prime powers need supplements to reach the nearest multiple of 3.
The difference between the squares of two consecutive odd integers is always divisible by:
Hint: Use algebraic expansion (2n + 3)² − (2n + 1)².
A solid wooden cube of side 6 cm is painted blue on all 6 faces and then cut into 1 cm unit cubes. How many unit cubes have EXACTLY TWO painted faces?
Hint: Cubes with 2 painted faces are located along the 12 edges minus the corner cubes.
If n² ends with the digit 6, what are the possible units digits of (n + 1)²?
Hint: Determine the units digit of n first when n² ends in 6.
A Pythagorean triplet has 16 as its smallest member. What is the sum of the other two members?
Hint: Apply the Pythagorean triplet formula (2m, m² − 1, m² + 1).
How many non-square natural numbers lie strictly between 45² and 46²?
Hint: Between n² and (n+1)², there are exactly 2n non-perfect squares.
Evaluate the square root: √(1 + 3 + 5 + 7 + ... + 49).
Hint: The sum of the first n odd numbers is n².
What is the smallest number by which 675 must be divided so that the quotient is a perfect cube?
Hint: Factor 675 into prime powers: 3³ × 5².
If x³ = 0.000216, what is the value of (10x)²?
Hint: Find the cube root of 216/1,000,000 first.
A square courtyard of side 32 m is to be paved with square tiles of side 80 cm. How many tiles are required?
Hint: Convert side lengths to centimetres and divide total area by single tile area.
Join the CT & AI Learning Community
Get new worksheets, quizzes, activities and AI learning resources on WhatsApp.
